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Dedekind’s Later Theory of Ideals

  • Jeremy Gray
Chapter
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In this chapter, we look at how Dedekind refined his own theory of ideals in the later 1870s, and then at the contrast with Kronecker

References

  1. Avigad, J.: Methodology and metaphysics in the development of Dedekind’s theory of ideals. In: Ferreirós, J., Gray, J.J. (eds.) The Architecture of Modern Mathematics, pp. 159–186. Oxford University Press, New York (2006)MATHGoogle Scholar
  2. Corry, L.: Modern algebra and the rise of mathematical structures. Science Networks. Historical Studies, vol. 17, 2nd edn. 2004. Birkhäuser, Basel (1996)Google Scholar
  3. Dedekind, R.: Über die Theorie der ganzen algebraischen Zahlen. Nachdruck des elften Supplements (Lejeune-Dirichlet 1893) (1964); preface by B. L. van der Waerden, Vieweg, BraunschweigGoogle Scholar
  4. Hilbert, D.: Die Theorie der algebraischen Zahlkörper (Zahlbericht). Jahresbericht der Deutschen Mathematiker-Vereinigung 4, 175–546 (1897); in Gesammelte Abhandlungen 1, 63–363, transl. I. Adamson, The theory of algebraic number fields, Berlin, Springer, 1998Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jeremy Gray
    • 1
    • 2
  1. 1.School of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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